Notes by Dr. Optoglass: The Resolution of the Human Eye

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Topics Covered:

The average and maximum resolutions of the human eye

PPI and DPI at various distances

Beauty is all very well at first sight; but who ever looks at it when it has been in the house three days? – George Bernard Shaw

As we have seen earlier, the average visual acuity of the human eye is one arc minute. The maximum possible is 0.4 arc minutes. It would be a very rare human indeed who can beat 0.4 arc minutes!

Therefore, we can safely say that the average resolution of a good eye is between 0.4 and 1 arc minute. Before these figures can be translated to pixels or displays, one needs to realize that the size of the pixel will vary with distance.

What’s the formula?

where

d is the distance in mm

? is the angle in degrees

A very young child can focus at about 2 inches, but the average adult can focus no closer than 4 inches (100 mm). We can assume the lowest value of d to be 100 mm. At this distance, the pixel/dot size p is 0.0116 mm or 11.6 microns – for 0.4 arc minutes. For 1 arc minute, it works out to be 29 microns.

An inch is 25.4mm. So how many of our pixels can fit into an inch? @0.4 arc minutes, it is 2190 ppi (dpi). @1 arc minute, it is 876 ppi (dpi)

Maximum Resolution of the Eye

So this is how it is. If a healthy adult brings any display screen or printed paper or whatever 4 inches (100 mm) from his or her face, the maximum resolution he/she can see at is 2190 ppi/dpi. It doesn’t get any better than this for 99.99% of us, except maybe during pre-kindergarten years.

But the legally accepted norm of 20/20 vision only asks for 876 ppi/dpi at 4 inches!

Let’s have some fun:

Magazines and Fine Art Prints

If the average reading distance is 1 foot (12 inches = 305 mm), p @0.4 arc minute is 35.5 microns or about 720 ppi/dpi. p @1 arc minute is 89 microns or about 300 dpi/ppi. This is why magazines are printed at 300 dpi – it’s good enough for most people. Fine art printers aim for 720, and that’s the best it need be. Very few people stick their heads closer than 1 foot away from a painting or photograph.

Computer Monitors

The average computer monitor viewing distance is about 2.5 feet (762 mm). p@0.4 is 89 microns or about 300 ppi/dpi. p@1 is 222 microns or about 115 ppi/dpi. Now you can understand why most consumer computer monitors are about 100 ppi, and most professional computer monitors are slightly higher, but not by much.

The new iPad (3) has a resolution of 264 ppi, which isn’t as good as 300 dpi print but is much better than the average computer monitor. The new Eizo 36.4″ professional air traffic control 4K monitor is at 128 ppi.

Home television

Assuming the average viewing distance for television is 6 feet (1830 mm), p@0.4 is about 120 ppi and p@1 is about 50 ppi.

Most consumer large screen LCD and LED panels are about 50 ppi to 90 ppi, and average about 72 ppi. Now you know why. If your television gets smaller in size, then the higher ppi doesn’t really help. This is why 1920×1080 (at 100 ppi at 6 feet for a 50″ LCD/LED television panel) is good enough. The eye can’t really resolve a lot more at 6 feet.

Cinema

The width of a cinema screen can vary from 30 to 70 feet (360″ to 840″, 9144 mm to 21,336 mm). The closest viewing distance recommended is about 40 feet (3x height) – 12,192 mm. If one is projecting 2K on these screens, the ppi is about 2.4 ppi to 5.7 ppi. If one is projecting 4K, it is about 5 ppi to 11.4 ppi.

Is this what the eye needs?
p@0.4 works out to be 1.4 mm or 18 ppi.
p@1 works out to be 3.5 mm or 7 ppi.

As you can see, 4K comes very close to what the human eye can fully resolve in a cinema screen at average viewing distances. Obviously, many people sit in the front row, and they’d definitely appreciate higher resolution. Which is why we are moving towards:

8K and UHDTV

A 30 to 70 feet screen at 8K (8192 horizontal) gives me from 9.75 ppi to 22.8 ppi. This resolution beats what the eye can resolve at these distances. The future belongs to 8K.

But, to get 18 ppi (the best possible resolution) for a 70 feet screen, we’ll need a horizontal resolution of 15120 or 16K. This is about 128 Megapixels. Is anybody working on this?

IMAX film is supposed to resolve between 10K to 12K (theoretical maximum)

I have pretty good vision, a little bit better than 20/20. According to this I can see about 75ppi at 6 feet.

I currently have a 55″ 1080p OLED TV. It has a pixel density of 40ppi. So, at a viewing distance of 6 feet having a 4K screen(assuming I’m watching 4K content) would make a difference. However, who sits 6 feet away from a 55″ screen? I sure wouldn’t. I currently sit 10 feet away from my 55″ (or 2.2x the screen size viewing distance). At that distance I wouldn’t be able to see 75ppi.

Don’t forget, as per the nyquist limit, you probably want to double the resolution so you don’t see jaggies in your diagonal lines. This is why printed text on paper is *still* better than HiDPI screens.

Sareesh Sudhakaran
it would just be very very helpful if for one single example the actual numbers were put into the formula so we could see it. the article is great overall but because that is missing it is very hard to grasp

I don’t understand the angle part of this? The angle is never listed for any of these calculations. How does that part work? What angles are you putting into the formula. Can you post examples that enter specifics for all of the variables rather than just the screen size and distance?

Under the “Home Television” section, you mentioned that a 1920×1080, 50″ display is 100 dpi. But, according to pxcalc.com, that combination only gets you to 38.4 dpi. How are you getting 100 dpi?? Thanks.